A magical and remarkable documentary about the free-roaming feline population of Istanbul.

Early in “Kedi,” Ceyda Torun’s splendidly graceful and quietly magical documentary about the multifaceted feline population of Istanbul, a human inhabitant of the city notes: “Dogs think people are God, but cats don’t. Cats know that people act as middlemen to God’s will. They’re not ungrateful. They just know better.” All of which might explain why so many of the movie’s four-legged subjects come across not as feral orphans who rely on the kindness of strangers, but rather as slumming royals who occasionally deign to interact with two-legged acolytes.

Indeed, another interviewee here swears that, after his fishing boat was damaged during a storm, a beneficent cat led him to a lost wallet containing just enough money to pay for repairs. “Whoever doesn’t believe this story,” the grateful beneficiary proclaims, “is a heathen in my book.”

Trust me: “Kedi” will make you a believer.

Torun, a Turkish-born filmmaker now based in the United States, and cinematographer Charlie Wuppermann, her partner in the production company Termite Films, take their audience on a leisurely yet purposeful journey throughout Istanbul (where Torun was raised) to examine a local phenomenon dating back to the heyday of the Ottoman Empire: Thousands of cats roam freely virtually everywhere and anywhere, peacefully co-existing with humans who learned long ago not to assume they are the masters in this situation.

Most of the felines are strays, proudly independent but more than willing to accept food and favors (and, more important, attentive petting) from the humans they choose to “adopt.” In turn, the humans — men, women, and children of all ages and backgrounds — admire and accept the autonomy of the cats. Even those who routinely feed, groom, and occasionally fret over the four-legged vagabonds who wander in and out of their lives respect the animals’ privacy — and freely admit that humans aren’t the only ones who benefit from this symbiotic relationship. “They absorb all your negative energy,” a shopkeeper says of the cats who sporadically show up at her door. “They do me good.”

Another interviewee claims that petting a cat can be as spiritually soothing as fingering prayer beads. But take care. “If you pet another cat,” he says while referencing his frequent guest, “she’ll get jealous and sulk.” Another problem to consider: As ambitious construction projects change the face of Istanbul, cats are displaced from their lairs whenever old buildings, or entire neighborhoods, are eliminated.

Cats are praised for everything from their therapeutic value to their usefulness as mousers throughout “Kedi.” But these heartfelt testimonials, delivered largely by unnamed admirers, don’t take up nearly as much screen time as footage devoted to the cats themselves. Lengthy, loving closeups alternate with remarkably fluid tracking shots as Torun and Wuppermann consider the elegant poise, casual indolence, and gritty resourcefulness of cats (and their kittens) going about their everyday lives.

The beautifully spare musical score by Kira Fontana provides the perfect accompaniment for what gradually emerges as a profoundly affecting meditation, at once dreamy and precise, on a force of nature — several forces of nature, actually, with paws and tails — surviving and thriving in an industrialized world.